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At Long Last, Physicists Calculate the Proton's Mass

It's one thing to know a fact, but it's another to explain it, as a curious advance in particle physics shows. Ever since the proton was discovered 89 years ago, physicists have been able to measure the mass of the particle--which, along with another called the neutron, makes up the atomic nucleus. But even with the best computers, theorists had not been able to start with a description of the proton's constituent parts and calculate its mass from scratch. Now, a team of theorists has reached that goal, marking the arrival of precision calculations of the ultracomplex "strong force" that binds nuclear matter.

"It's a really big deal," says John Negele, a theorist at the Massachusetts Institute of Technology in Cambridge. "It's the first time that we've really had this kind of confidence that everything is being done right."

Like a troubled teenager, the proton is a mess inside and just about impossible to figure out. In the 1970s, experimenters discovered that the proton and the neutron, known collectively as nucleons, consist of more-fundamental particles called quarks and gluons, which are the basic elements of a theory called quantum chromodynamics (QCD). In the simplest terms, a proton contains two "up" type quarks and one "down" type quark, with gluons zipping among them to bind them with the strong nuclear force. (The neutron contains two downs and an up.) In reality, a nucleon is much more complicated.

Thanks to the uncertainties of quantum mechanics, myriad gluons and quark-antiquark pairs flit in and out of existence within a nucleon. All of these "virtual" particles interact in a frenzy of pushing and pulling that's nearly impossible to analyze quantitatively. "Everything interacts with everything," says Laurent Lellouch, a theorist with the French National Center for Scientific Research at the Center for Theoretical Physics in Marseille and one of 12 physicists from France, Germany, and Hungary who performed the new calculations. Ninety-five percent of the mass of a nucleon originates from these virtual particles.

To simplify matters, the team took a tack pioneered in the late 1970s called lattice QCD. Within their computer programs, the researchers modeled space not as continuous but as a three-dimensional array of points. They also modeled time as passing in discrete ticks, as opposed to flowing smoothly. This turns space and time into a lattice of points. The researchers then confined the quarks to the points in the lattice and the gluons to the links between the points. The lattice sets a shortest distance and time for the interactions, greatly simplifying the problem.

Still, the computation involves millions of variables and requires supercomputers. Only since about 2000 have researchers attempted to include not just all of the gluons but the fleeting quark-antiquark pairs as well. The latest work, reported today in Science, incorporates a variety of conceptual improvements to obtain estimates of the mass of the nucleon and nine other particles made of up, down, and slightly heavier "strange" quarks accurate to within a couple of percent.

This isn't the first computational tour de force for particle physicists. Five years ago, others made equally precise calculations of more esoteric quantities--somewhat easier to calculate--such as those that govern the decay of a particle called a D+ meson, which contains a down antiquark and a heavy "charm" quark, notes Christine Davies, a theorist at the University of Glasgow in the U.K. Still, she says, the calculation of the well-known masses highlights the ability of lattice QCD to make accurate predictions for the strong force. "This is all good news for lattice QCD," Davies says, "because there are lots of things that we want to calculate that experimenters haven't already measured." For example, Negele says, physicists still don't know distribution of the virtual particles inside the proton or the origin of its spin.